Three forms of normal to $y^2$ = 4ax:

1. Point form: y - y1 = -($\frac{y1}{2a}$)(x - x1)
2. Slope form: y = mx - 2am - $am^3$
3. Parametric: y + tx = 2at + $at^3$ at parameter t

From an external point, at most 3 normals can be drawn. The parameters satisfy: t1+t2+t3 = 0, t1t2+t2t3+t3t1 = $\frac{2a-h}{a}$ (where h is x-coordinate of external point), t1t2t3 = -k/a (where k is y-coordinate).